Abstract
An investigation of the asymptotic behavior of the logarithm of the number of simple bases and the number of functions of n variables in Post's classes F ui (i =1, 4, 5, 8; μ≥ 2).
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Literature cited
E. Post, Two-Valued Iterative Systems, Princeton Univ. Press, Oxford Univ. Press, London (1941).
S. V. Yablonskii, G. P. Gavrilov, and V. B. Kudryavtsev, Functions of the Algebra of Logic and Post's Classes [in Russian], Moscow (1966).
G. A. Shestopal, “The number of simple bases of Boolean functions,” Dokl. Akad. Nauk SSSR,140, No. 2, 314–317 (1961).
G. A. Shestopal, “Simple bases in closed classes of functions of the algebra of logic,” Dokl. Akad. Nauk SSSR,168, No. 5, 1023–1026 (1966).
A. Salomaa, “On the number of simple bases of the set of functions over a finite domain,” Turun Yliopiston, Julkaisuja, Saria-Series Al, No. 52, 3–4 (1962).
S. V. Yablonskii, “The superposition of functions in Pk,” in: Problems of Cybernetics, No. 9, 337–340 (1963).
V. B. Alekseev, “Simple bases of k-valued logic,” Matem. Zametki,5, No. 4, 471–482 (1969).
E. Yu. Zakharov and S. V. Yablonskii, “Some properties of essential functions of Pk,” in: Problems of Cybernetics, No. 12, 247–252 (1964).
G. Hansel, “Sur le nombre des functions Booléenes monotones de n variables,” C. R. Acad. Sci. (A),262, 1088 (1966).
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Translated from Matematicheskie Zametki, Vol. 8, No. 1, pp. 105–114, July, 1970.
The author wishes to thank V. B. Kudryavtsev, who directed this work.
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Sheinbergas, I.M. Simple bases and the number of functions in certain classes introduced by Post. Mathematical Notes of the Academy of Sciences of the USSR 8, 528–533 (1970). https://doi.org/10.1007/BF01093447
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DOI: https://doi.org/10.1007/BF01093447